Sequences

Front

What is a sequence in mathematics?

Back

A sequence is an ordered list of numbers that follow a specific pattern or rule.

Front

Define the term 'common difference' in an arithmetic sequence.

Back

The common difference is the constant amount that each term in an arithmetic sequence increases or decreases by.

Front

What does a₁ represent in a sequence?

Back

a₁ represents the first term of the sequence.

Front

How do you find the first four terms of the sequence defined by a_n = 4(5)^n-1?

Back

Substitute n=1,2,3,4 into the formula to get the terms: 4, 20, 100, 500.

Front

What is the formula for finding the nth term of an arithmetic sequence?

Back

The nth term can be found using the formula: a_n = a₁ + (n-1)d, where d is the common difference.

Front

Find the first four terms of the sequence defined by a_n+1 = a_n + 9, where a₁ = -2.

Back

The first four terms are: -2, 7, 16, 25.

Front

What is the difference between an arithmetic sequence and a geometric sequence?

Back

An arithmetic sequence has a constant difference between terms, while a geometric sequence has a constant ratio between terms.

Front

How do you find the first four terms of the sequence defined by a_n = a_(n-1) - 18, where a₁ = 10?

Back

The first four terms are: 10, -8, -26, -44.

Front

What is a geometric sequence?

Back

A geometric sequence is a sequence where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.

Front

Identify the common difference in the sequence: 10, 20, 30, 40, ...

Back

The common difference is 10.